A stochastic theory of non-ideal behaviour

Abstract

The stochastic theory described in Part I is extended here to the case of a ternary system [A, B, C] at equilibrium. Using the microenvironment and the quasi-chemical (QC) approximations, we derive equations to estimate the differences in chemical potentials in terms of the three pair interaction parameters ω_AB, ω_AC and ω_BC. Alternative equations for calculating these differences have been derived by Bell, using the QC approximation alone. We show that, within the framework of the QC approximation, these estimations are essentially unaffected by our additional microenvironment approximation. Furthermore, the results are in excellent agreement with values obtained with the help of exact equations using computer simulation of ternary lattices at equilibrium.

The capability of the theory to predict liquid-liquid equilibria in real ternary systems is examined. Experimental data on binary systems permit us to evaluate the values of the pair interaction parameters ω_AB, ω_AC and ω_BC. The theory is capable of describing a variety of phenomena encountered in the experiment. The eruption of an island curve with a two-phase region is accounted for by the theory without requiring the addition of a ternary interaction parameter. In all the cases reported, our results are in better agreement with experiment than those obtained from the widely used Van Laar or NRTL equations, which have moreover the weakness of dealing with a relatively large number of parameters. In this connection, it is worth stressing that the three pair interaction parameters ω, used in our theory, represent the reduced interaction energies between molecules of different type. Therefore, if experiments could provide a complete set of values for these interaction energies, our description of a ternary system would constitute a ‘zero parameter’ theory.